Financial Risk Manager Part 1

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Explanation:

The correct answer to the question is B, which is USD 557. The explanation for this answer is based on the delta-normal approach to calculate the Value at Risk (VaR) for non-linear derivatives such as options. The delta-normal approach assumes that the changes in the price of the underlying asset are normally distributed and uses the delta of the option to approximate the change in the option's price.

Here's a step-by-step breakdown of the calculation:

Calculate the 1-day 95% VaR for 1 share of the underlying stock:
- The daily stock return volatility is given as 1.82%.
- The z-score for a 95% confidence level is 1.645 (from the standard normal distribution).
- The current stock price is USD 62.
- The formula to calculate the VaR for 1 share is: VaR = Volatility * z-score * Stock Price.
- Plugging in the values: VaR = 0.0182 * 1.645 * 62 = USD 1.8562.
Calculate the VaR for one option:
- The delta of the option is 0.5, which represents the sensitivity of the option's price to a change in the stock price.
- The VaR of one option is the delta times the VaR of 1 share of the stock: 0.5 * 1.8562 = USD 0.9281.
Calculate the 1-day 95% VaR for the entire position:
- The portfolio manager bought 600 call options.
- The total VaR for the position is the VaR of one option multiplied by the number of options: 0.9281 * 600 = USD 556.86, which is approximately USD 557.

The other options provided are incorrect for the following reasons:

Option A (USD 54) is incorrect because it ignores the delta and uses the call option price instead of the stock price to determine the VaR.
Option C (USD 787) is incorrect because it calculates the VaR at the 99% confidence level instead of the 95% level.
Option D (USD 1,114) is incorrect because it does not apply the delta to the formula.

This question tests the understanding of the delta-normal approach and its application to calculate VaR for non-linear derivatives, as outlined in the reference material by the Global Association of Risk Professionals.

Explanation:

Here's a step-by-step breakdown of the calculation:

Calculate the 1-day 95% VaR for 1 share of the underlying stock:
- The daily stock return volatility is given as 1.82%.
- The z-score for a 95% confidence level is 1.645 (from the standard normal distribution).
- The current stock price is USD 62.
- The formula to calculate the VaR for 1 share is: VaR = Volatility * z-score * Stock Price.
- Plugging in the values: VaR = 0.0182 * 1.645 * 62 = USD 1.8562.
Calculate the VaR for one option:
- The delta of the option is 0.5, which represents the sensitivity of the option's price to a change in the stock price.
- The VaR of one option is the delta times the VaR of 1 share of the stock: 0.5 * 1.8562 = USD 0.9281.
Calculate the 1-day 95% VaR for the entire position:
- The portfolio manager bought 600 call options.
- The total VaR for the position is the VaR of one option multiplied by the number of options: 0.9281 * 600 = USD 556.86, which is approximately USD 557.

The other options provided are incorrect for the following reasons:

Option A (USD 54) is incorrect because it ignores the delta and uses the call option price instead of the stock price to determine the VaR.
Option C (USD 787) is incorrect because it calculates the VaR at the 99% confidence level instead of the 95% level.
Option D (USD 1,114) is incorrect because it does not apply the delta to the formula.

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A portfolio manager has acquired 600 call options for a non-dividend-paying stock. Each call option carries a strike price of USD 60 and was bought at a cost of USD 3. The stock's current trading price is USD 62, with a daily volatility rate of 1.82%. The options have a delta value of 0.5. Using the delta-normal method for Value at Risk (VaR) estimation, determine the approximate 1-day 95% VaR for this portfolio.

Exam-Like

USD54

14.4%

USD557

58.3%

USD787

15.2%